3,654 research outputs found
Regularity scalable image coding based on wavelet singularity detection
In this paper, we propose an adaptive algorithm for scalable wavelet image coding, which is based on the general feature, the regularity, of images. In pattern recognition or computer vision, regularity of images is estimated from the oriented wavelet coefficients and quantified by the Lipschitz exponents. To estimate the Lipschitz exponents, evaluating the interscale evolution of the wavelet transform modulus sum (WTMS) over the directional cone of influence was proven to be a better approach than tracing the wavelet transform modulus maxima (WTMM). This is because the irregular sampling nature of the WTMM complicates the reconstruction process. Moreover, examples were found to show that the WTMM representation cannot uniquely characterize a signal. It implies that the reconstruction of signal from its WTMM may not be consistently stable. Furthermore, the WTMM approach requires much more computational effort. Therefore, we use the WTMS approach to estimate the regularity of images from the separable wavelet transformed coefficients. Since we do not concern about the localization issue, we allow the decimation to occur when we evaluate the interscale evolution. After the regularity is estimated, this information is utilized in our proposed adaptive regularity scalable wavelet image coding algorithm. This algorithm can be simply embedded into any wavelet image coders, so it is compatible with the existing scalable coding techniques, such as the resolution scalable and signal-to-noise ratio (SNR) scalable coding techniques, without changing the bitstream format, but provides more scalable levels with higher peak signal-to-noise ratios (PSNRs) and lower bit rates. In comparison to the other feature-based wavelet scalable coding algorithms, the proposed algorithm outperforms them in terms of visual perception, computational complexity and coding efficienc
Multiobjective programming for type-2 hierarchical fuzzy inference trees
This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an
optimum tree-like structure. Specifically, a natural hierarchical structure that accommodates simplicity by
combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure
provides a high degree of approximation accuracy. The construction of HFIT takes place in two phases.
Firstly, a nondominated sorting based multiobjective genetic programming (MOGP) is applied to obtain a
simple tree structure (low modelās complexity) with a high accuracy. Secondly, the differential evolution
algorithm is applied to optimize the obtained treeās parameters. In the obtained tree, each node has a
different inputās combination, where the evolutionary process governs the inputās combination. Hence,
HFIT nodes are heterogeneous in nature, which leads to a high diversity among the rules generated
by the HFIT. Additionally, the HFIT provides an automatic feature selection because it uses MOGP
for the treeās structural optimization that accept inputs only relevant to the knowledge contained in
data. The HFIT was studied in the context of both type-1 and type-2 FISs, and its performance was
evaluated through six application problems. Moreover, the proposed multiobjective HFIT was compared
both theoretically and empirically with recently proposed FISs methods from the literature, such as
McIT2FIS, TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the
obtained results, it was found that the HFIT provided less complex and highly accurate models compared
to the models produced by most of the other methods. Hence, the proposed HFIT is an efficient and
competitive alternative to the other FISs for function approximation and feature selectio
Separable Gaussian Neural Networks: Structure, Analysis, and Function Approximations
The Gaussian-radial-basis function neural network (GRBFNN) has been a popular
choice for interpolation and classification. However, it is computationally
intensive when the dimension of the input vector is high. To address this
issue, we propose a new feedforward network - Separable Gaussian Neural Network
(SGNN) by taking advantage of the separable property of Gaussian functions,
which splits input data into multiple columns and sequentially feeds them into
parallel layers formed by uni-variate Gaussian functions. This structure
reduces the number of neurons from O(N^d) of GRBFNN to O(dN), which
exponentially improves the computational speed of SGNN and makes it scale
linearly as the input dimension increases. In addition, SGNN can preserve the
dominant subspace of the Hessian matrix of GRBFNN in gradient descent training,
leading to a similar level of accuracy to GRBFNN. It is experimentally
demonstrated that SGNN can achieve 100 times speedup with a similar level of
accuracy over GRBFNN on tri-variate function approximations. The SGNN also has
better trainability and is more tuning-friendly than DNNs with RuLU and Sigmoid
functions. For approximating functions with complex geometry, SGNN can lead to
three orders of magnitude more accurate results than a RuLU-DNN with twice the
number of layers and the number of neurons per layer
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
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